Gravitational Instability of a Magnetic Rotating Disk with Ohmic Dissipation and Ambipolar Diffusion

Abstract

Abstract We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects: Ohmic dissipation and ambipolar diffusion. Our results show that there is always a preferred lengthscale and associated minimum timescale for gravitational instability. The addition of rotation leads to a generalized Toomre criterion (that includes a magnetic dependence) and modified lengthscales and timescales for collapse. We show that both the nonideal MHD effects qualitatively behave in a similar way but have quantitative differences. We apply our results to protostellar disk properties in the early embedded phase and find that the preferred scale of instability can significantly exceed the thermal (Jeans) scale and the peak preferred fragmentation mass is likely to be ∼10–90M Jup.